Mice problem

In mathematics, the mice problem is a continuous pursuit-evasion problem in which a number of mice (or insects, dogs, missiles, etc.) are considered to be placed at the corners of a regular polygon. In the classic setup, each then begins to move towards its immediate neighbour (clockwise or anticlockwise). The goal is often to find out at what time the mice meet.

For the Monty Python sketch, see The Mouse Problem.
Four mice
Three mice
Six mice

The most common version has the mice starting at the corners of a unit square, moving at unit speed. In this case they meet after a time of one unit, because the distance between two neighboring mice always decreases at a speed of one unit. More generally, for a regular polygon of unit-length sides, the distance between neighboring mice decreases at a speed of , so they meet after a time of .[1][2]

Path of the mice

For all regular polygons, each mouse traces out a pursuit curve in the shape of a logarithmic spiral. These curves meet in the center of the polygon.[3]

gollark: What do you mean "open source"? Open source software is able to run it fully? Someone's released all the hardware design files?
gollark: Error correcting codes at least.
gollark: I doubt it. There's presumably some intermediate encoding step going on.
gollark: If you have a video recorder program which does that, just take the output and mux out the video stream.
gollark: You can make Desmos draw π multiples on the axes?!

References
  1. Gamow, George; Stern, Marvin (1958). Puzzle Math. Viking Press. pp. 112–114.
  2. Lucas, Édouard (1877). "Problem of the Three Dogs". Nouv. Corresp. Math. 3: 175–176.
  3. Weisstein, Eric W. "Mice Problem". MathWorld.


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